document.write( "Question 1207798: Rico's and Maris's age gap is 25 years.
\n" ); document.write( "4 years from now, Rico's age will be 5 years less than twices maris's age \n" ); document.write( "
Algebra.Com's Answer #845898 by ikleyn(52787)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "Rico's and Maris's age gap is 25 years.
\n" ); document.write( "4 years from now, Rico's age will be 5 years less than \"highlight%28cross%28twices%29%29\" twice maris's age.
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\n" ); document.write( "\n" ); document.write( "        The question absents,  which is   \"highlight%28highlight%28outrageous%29%29\".\r
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\n" ); document.write( "\n" ); document.write( "        In the post by @MathLover1,  the solution is not complete.
\n" ); document.write( "        I came to bring a complete analysis.\r
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document.write( "As you read the problem, it produces two equations.\r\n" );
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document.write( "    |R-M| = 25          (1)     (\"the gap is 25 years\")\r\n" );
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document.write( "     R+4 = 2(M+4)-5     (2)     (\"4 years from now\")\r\n" );
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document.write( "Notice that equation (1) is an absolute value equation.\r\n" );
document.write( "So, equation (1) is equivalent to system of two equations\r\n" );
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document.write( "    R - M = 25          (1a)\r\n" );
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document.write( "  or\r\n" );
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document.write( "    R - M = -25         (1b)\r\n" );
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document.write( "It means that we should consider two cases and solve two associated systems.\r\n" );
document.write( "One system is\r\n" );
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document.write( "     R - M = 25,         (1a)\r\n" );
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document.write( "     R + 4 = 2(M+4)-5.    (2)\r\n" );
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document.write( "Another system is\r\n" );
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document.write( "     R - M = -25,        (1b)\r\n" );
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document.write( "     R + 4 = 2(M+4)-5.    (2)\r\n" );
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document.write( "Let start solving first system.\r\n" );
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document.write( "From equation (2),\r\n" );
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document.write( "     R = 2M - 1.         (3)\r\n" );
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document.write( "Substitute it into equation (1a)\r\n" );
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document.write( "     (2M-1) - M = 25.\r\n" );
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document.write( "It implies\r\n" );
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document.write( "      2M - M = 25 + 1\r\n" );
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document.write( "         M   =   26.\r\n" );
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document.write( "Substitute it into equation (3) \r\n" );
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document.write( "    R = 2M - 1 = 2*26 - 1 = 51.\r\n" );
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document.write( "So, Maris is 26 years old; Rico is 51 years old.\r\n" );
document.write( "At this point, we complete working with the first system and start working with the second system.\r\n" );
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document.write( "We again substitute (3) into equation (1b)\r\n" );
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document.write( "    (2M-1) - M = -25\r\n" );
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document.write( "      M        = -25 + 1 = -24.\r\n" );
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document.write( "The age is always positive, it can not be negative, so we deny this possibility, at all.\r\n" );
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document.write( "ANSWER.  The problem has a unique solution: Maris is 26 years old; Rico is 51 years old.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved in full and completely.\r
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\n" ); document.write( "\n" ); document.write( "The lesson to learn.\r
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\n" ); document.write( "\n" ); document.write( "        The term  \" gap between two values \"  means the absolute value of the difference.\r
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\n" ); document.write( "\n" ); document.write( "        So, the system of equations should include an absolute value equation.\r
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\n" ); document.write( "\n" ); document.write( "        In some sense,  this problem is a  TRAP,  and if you did not recognize this trap \r
\n" ); document.write( "\n" ); document.write( "        with the absolute value equation,  then you failed.\r
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\n" ); document.write( "\n" ); document.write( "Added later,  after seeing comment by  @greenestamps to my solution.\r
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\n" ); document.write( "\n" ); document.write( "The problem says\r
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document.write( "    Rico's  and  Maris'  age gap is  25  years.\r\n" );
document.write( "    4  years from now,  Rico's age will be  5  years less than twice maris' age.\r\n" );
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\n" ); document.write( "\n" ); document.write( "In his comment,  @greenestamps writes  \" the information in the second sentence tells you that  Rico is older\".\r
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\n" ); document.write( "\n" ); document.write( "But the problem does not say it explicitly.  It says something different.\r
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\n" ); document.write( "\n" ); document.write( "It becomes clear not from this sentence,  but from analysis of the full system of equations.\r
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\n" ); document.write( "\n" ); document.write( "So,  the meaning of this @greenestamps' comment is dark to me.
\n" ); document.write( "I do not agree with it,  and I do not think that it is correct.\r
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\n" ); document.write( "\n" ); document.write( "To post by  Edwin.\r
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\n" ); document.write( "\n" ); document.write( "         Edwin,  can you explain,  please,  how your post helps us to treat this problem ?\r
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\n" ); document.write( "\n" ); document.write( "Edwin, offhand I requested Google for these keywords \r
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\n" ); document.write( "\n" ); document.write( "        \"Rico's and Maris's age gap is 25 years.
\n" ); document.write( "        4 years from now, Rico's age will be 5 years less than twices maris's age\".\r
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\n" ); document.write( "\n" ); document.write( "I got several references/links\r
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\n" ); document.write( "\n" ); document.write( "https://math.he.net/question/1d4c2a3ddd3855cf85182d952bc3247db2813e73\r
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\n" ); document.write( "\n" ); document.write( "https://www.facebook.com/photo.php?fbid=997207245743634&id=100063631043464&set=a.518642723600091\r
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\n" ); document.write( "\n" ); document.write( "https://www.gauthmath.com/solution/1805163005838341/Maris-and-Rico-announced-their-breakup-Many-assume-that-the-reason-for-the-break\r
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\n" ); document.write( "\n" ); document.write( "https://www.gauthmath.com/solution/1805071070479366/PROBLEM-Maris-and-Rico-announced-their-breakup-Many-assume-that-the-reason-for-t\r
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\n" ); document.write( "\n" ); document.write( "So, I am very far from assuming that poor unfortunate foreign visitors send
\n" ); document.write( "this problem everywhere in the Internet out of curiosity and desire for knowledge.\r
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\n" ); document.write( "\n" ); document.write( "My hypothesis is that they either participate in training AI or
\n" ); document.write( "fill some other web-sites this way by collecting solutions from everywhere.\r
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\n" ); document.write( "\n" ); document.write( "All what they really do, is copying, pasting and submitting, without reading;
\n" ); document.write( "therefore, they even do not notice when they miss the question.
\n" ); document.write( "They simply do not read what they post.\r
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\n" ); document.write( "\n" ); document.write( "Because making sense is not a goal of their job, at all.\r
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\n" ); document.write( "\n" ); document.write( "Their job is copy/paste/submit and do it fast - nothing more.\r
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